What is the value of the x variable in the solution to the following system of equations for 4x+ 2y =6 x-y=3

x = -1

Step-by-step explanation:

To start with, we can solve for y in 4x + 2y = 6. We want to find the y so we can insert it into our second equation to find out what our x-variable is.

We are going to want to get y by itself, so we can subtract the positive 4x and move it onto the right side.

4x + 2y = 6

2y + 4x - 4x = 6 - 4x

2y = 6 - 4x

2y = -4x + 6

Now that we have this, we still want to get y by itself. Y has a coefficient in front of it, so we are going to want to get rid of that. Because y is being multiplied by 2, we can do the opposite and divide the entire equation by 2. The 2y would be divided by 2, the -4x would be divided by 2, and the 6 would be divided by 2.

This leaves us with: y = -2x + 3.

Now that we know what our y is equal to, we can insert this into our second equation of x - y = 3.

x - y = 3

Let's replace y with what we now know y is equivalent to: -2x + 3.

x - (-2x) + 3.

Subtracting a negative number is equivalent to addition, so we can turn that into an addition sign now:

x + 2x + 3

3x + 3 = 0

Remembering the question, we want to get the x variable alone because that is what we want to solve for. Let's do that now by moving the 3 onto the right side. Since we are adding it, we can subtract it to move it over. Like this:

3x + 3 = 0

3x + 3 - 3 = 0 - 3

3x = -3

Now, like we did in the beginning of this problem, we want the x alone, and because it is being multiplied by x, we can divide the entire problem by 3. -3 will get divided by 3 which will give us -1.

x = -1